The government says it has the LTTE confined in an area of less than 100sq km along a coastal jungle stretch in the northeast.
In the statement, issued on Monday in the name of its political wing leader B Nadesan, the LTTE appealed to foreign powers to step in and broker a truce.
"The international community must do everything in its power to bring a ceasefire so that the miseries of the Tamils ... are brought to an end," it said.
The LTTE said "the international community should apply pressure on the Sri Lankan government to seek not a military, but a political, solution to the ethnic conflict".
The statement said the LTTE had asked the UN and a quartet consisting of the US, the European Union, Japan and one-time mediator Norway to pressure the Sri Lankan government into accepting a ceasefire.
The quartet had earlier asked the LTTE to negotiate terms of surrender, saying that the group was fast losing ground in the face of a major government military offensive.
But in its statement, the LTTE rejected calls to disarm.
"The world should take note that calls for the LTTE to lay down its arms and surrender is not helpful for resolving the conflict."
The LTTE claimed that dozens of people were being killed and wounded daily in the ongoing heavy fighting in the northeast.
"The protection of the Tamil people is dependent on the arms of the LTTE," the statement said.
"When a permanent political solution is reached for the Tamil people with the support and the guarantee of the international community, the situation will arise where there will be no need for the arms of the LTTE."
However, the statement made it clear that the LTTE still wanted a separate state for Sri Lanka's ethnic Tamil minority.
"The international community, though it is hesitant to support the political aspirations of the Tamil people for an independent state, it must re-examine our point that an independent state is the only permanent solution to the Tamil-Sinhala conflict."
Meanwhile, on the ground, there has been no let-up in the violence.
The defence ministry said on Sunday that the number of people killed in an LTTE attack on a Sinhalese village in the east of the country had risen to 21.
Fighters stormed the village of Kirimetiya late on Saturday and opened fire on residents, the ministry said.
The bodies of 14 people were brought to the main hospital in the district capital of Ampara, a hospital official told the AFP news agency.
No independent reports about the attack were available from the remote village, which is located in an area controlled by the LTTE until 2007.
The Sri Lankan military separately said security forces killed at least 65 Tamil Tigers in a week of intense fighting.
Also on Sunday, defence officials released footage of Friday's raids by LTTE aircraft on Colombo, Sri Lanka's largest city.
The LTTE has said the "suicide missions", during which one aircraft flew into a tax office building, were a success.
But the government said that its footage, part of which shows a light aircraft flying into a building and exploding, proves the two aircraft were brought down by anti-aircraft fire.
The LTTE probably intended to hit the air force headquarters and an air base, government officials said.